giải giúp em pt này vs \(\frac{x-27}{27}+\frac{x-36}{24}+\frac{x}{30}=4\)
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DL
6 tháng 5 2018
pt \(\Leftrightarrow\left(\frac{x-2}{27}-1\right)+\left(\frac{x-3}{26}-1\right)+\left(\frac{x-4}{25}-1\right)+\left(\frac{x-5}{24}-1\right)+\left(\frac{x-44}{5}+3\right)=0\)
\(\Leftrightarrow\frac{x-29}{27}+\frac{x-29}{26}+\frac{x-29}{25}+\frac{x-29}{24}+\frac{x-29}{5}=0\)
\(\Leftrightarrow\left(x-29\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\right)=0\)
Mà \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\ne0\)
\(\Rightarrow x-29=0\Leftrightarrow x=29\)
2 tháng 3 2020
\(a,⇔\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)
\(⇔(x-23)(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27})=0\)
\(⇔x-23=0\) (vì \(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}>0\))
\(⇔x=23\)
\(b,⇔\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}+\frac{x+100}{95}=0\)
\(⇔(x+100)(\frac{1}{98}+\frac{1}{97}+\frac{1}{96}+\frac{1}{95})=0\)
\(⇔x+100=0\) (vì \(\frac{1}{98}+\frac{1}{97}+\frac{1}{96}+\frac{1}{95}>0\))
\(⇔x=-100\)
\(c,⇔(\frac{x+1}{2012}+1)+(\frac{x+2}{2011}+1)=(\frac{x+3}{2010}+1)+(\frac{x+4}{2009}+1)\)
\(⇔\frac{x+2013}{2012}+\frac{x+2013}{2011}-\frac{x+2013}{2010}-\frac{x+2013}{2009}=0\)
\(⇔(x+2013)(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009})=0\)
\(⇔x+2013=0\) (vì \(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}<0\))
\(⇔x=-2013\)
KS
2 tháng 3 2020
\(\frac{201-x}{99}+\frac{203}{97}=\frac{205}{95}+3\)
\(\frac{x-45}{55}+\frac{x-47}{53}=\frac{x-55}{45}+\frac{x-53}{47}\)
\(\frac{2-x}{2010}-1=\frac{1-x}{2011}-\frac{x}{2012}\)
Giúp mk với ạ
5 tháng 3 2015
pạn -1 vào mỗi phân số là xong. Rùi ra x\(\frac{x-2015}{1986}\)+\(\frac{x-2015}{1988}\)+ \(\frac{x-2015}{1990}\)+...+\(\frac{x-2015}{x1996}\)-\(\frac{x-2015}{29}\)-\(\frac{x-2015}{27}\)-...\(\frac{x-2015}{19}\)=0
<=>(x-2015)(\(\frac{1}{1986}\)+\(\frac{1}{1988}\)+... -\(\frac{1}{19}\))=0...(mà \(\frac{1}{1986}\)+...- \(\frac{1}{19}\) khác 0)
=>x-2015=0
<=> x=2015
NK
0
TT
5
28 tháng 7 2018
Qui đồng rồi khử mẫu, ta được:
\(4x+12.\left(27-x\right)=15x+5.\left(27-x\right)\)
\(\Leftrightarrow4x+324-12x=15x+135-5x\)
\(\Leftrightarrow4x-12x-15x+5x=135-324\)
\(\Leftrightarrow-18x=-189\Leftrightarrow x=\frac{21}{2}=10,5\)
Vậy x = 10,5
28 tháng 7 2018
\(\frac{x}{15}+\frac{27-x}{5}=\frac{x}{4}+\frac{27-x}{12}\)
\(\frac{x}{15}+\frac{3\left(27-x\right)}{15}=\frac{3x}{12}+\frac{27-x}{12}\)
\(\frac{x}{15}+\frac{81-3x}{15}=\frac{3x}{12}+\frac{27-x}{12}\)
\(\frac{x+81-3x}{15}=\frac{3x+27-x}{12}\)
\(\frac{-2x+81}{15}=\frac{2x+27}{12}\)
\(12\left(-2x+81\right)=15\left(2x+27\right)\)
\(-24x+972=30x+405\)
\(972-405=30x+24x\)
\(567=54x\)
\(x=567:54\)
\(x=10,5\)
NM
4
21 tháng 5 2017
\(x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}}=2\)
\(\Leftrightarrow\sqrt{x+\frac{1}{4}+2.\sqrt{x+\frac{1}{4}}.\frac{1}{2}+\frac{1}{4}}=2-x\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x+\frac{1}{4}}+\frac{1}{2}\right)^2}=2-x\)
\(\Leftrightarrow\sqrt{x+\frac{1}{4}}+\frac{1}{2}=2-x\)
\(\Leftrightarrow\sqrt{x+\frac{1}{4}}=\frac{3}{2}-x\)(\(x\le\frac{3}{4}\))
\(\Leftrightarrow x^2-4x+2=0\)
\(\Leftrightarrow\hept{\begin{cases}2-\sqrt{2}\\2+\sqrt{2}\left(l\right)\end{cases}}\)
NH
3
BA
22 tháng 2 2020
\(\frac{x-12}{21}+\frac{x-10}{23}=\frac{x-8}{25}+\frac{x-6}{27}\)
\(\Leftrightarrow\frac{x-12-21}{21}+\frac{x-10-23}{23}-\frac{x-8-25}{25}-\frac{x-6-27}{27}=0\)
\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}-\frac{x-33}{25}-\frac{x-33}{27}=0\)
\(\Leftrightarrow\left(x-33\right)\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)=0\)
Vif \(\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)\ne0\)
\(\Rightarrow x-33=0\)
\(\Rightarrow x=33\)
NH
22 tháng 2 2020
\(\frac{x-12}{21}+\frac{x-10}{23}=\frac{x-8}{25}+\frac{x-6}{27}\)
\(\Leftrightarrow\frac{x-12}{21}+1+\frac{x-10}{23}+1=\frac{x-8}{25}+1+\frac{x-6}{27}+1\)
\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}=\frac{x-33}{25}+\frac{x-33}{27}\)
\(\Leftrightarrow\frac{x-33}{21}+\frac{x-33}{23}-\frac{x-33}{25}-\frac{x-33}{27}=0\)
\(\Leftrightarrow\left(x-33\right)\left(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\right)=0\)
Mà \(\frac{1}{21}+\frac{1}{23}-\frac{1}{25}-\frac{1}{27}\ne0\)
\(\Rightarrow x-33=0\)
\(\Leftrightarrow x=33\)
\(\Leftrightarrow\dfrac{x}{27}-1+\dfrac{x}{24}-\dfrac{3}{2}+\dfrac{x}{30}=4\)
\(\Leftrightarrow x\left(\dfrac{1}{27}+\dfrac{1}{24}+\dfrac{1}{30}\right)=\dfrac{13}{2}\)
\(\Leftrightarrow x=\dfrac{\dfrac{13}{2}}{\dfrac{1}{27}+\dfrac{1}{24}+\dfrac{1}{30}}\)\(=\dfrac{7020}{121}\)
Vậy pt có tập nghiệm là S=\(\left\{\dfrac{7020}{121}\right\}\).
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